The main problem would be his legal and physical inability to do anything of the kind: legal because election of the emperor of the HRE was done by the electors and physical because at that time the Pope was still ruling his own state only because Nappy let him (and it would not be for long). An idea that the Pope is declaring creation of his own empire confined to the papal states belongs either to "what Pius VII could do if he became insane before his insanity is being noticed" or to good old ASBs.
Rather difficult with Napoleon controlling Italy.
As a trade partner the papal states at that time hardly were of any serious value to anybody.
By 1806 the Americans were more than vaguely aware of Napoleon's existence, which means that they would not bite even even the schema is offered.